Empty homes, called Akiya in Japanese, due to an aging population and declining birthrate is very serious problem in the aging society of modern Japan. The current proportion of empty home in Japan is 13.5%, but it is expected to be increased up to 30.2% nationwide in 2033, implying that Akiya will have a serious impact on the economy as well as the national finance. Indeed, Detroit city in USA was financially collapsed by 29.3% empty homes caused by the decline of the automobile industry. Currently, the Japanese government has started a countermeasure for decreasing the empty homes, but the effect is completely uncertain. Therefore, we here develop a mathematical model including an effective utilization of empty homes and consider the future transition of empty homes. Using the model, we suggest optimal policies by which we can reduce empty homes most effectively, with regard to government tax system and subsidy for the effective utilization of empty homes. This study shows a new framework of mathematical model to be applied for solving a social and economic problem in real world.